In order to perform a combustion control based on a cetane value of the fuel, various apparatus detecting the cetane value with high accuracy are proposed. For example, JP-2009-144528A (U.S. Pat. No. 7,987,696B2) shows a fuel property detecting apparatus which performs a specific fuel injection in which a first quantity of the fuel and a second quantity of the fuel are injected to compute a physical quantity variation sensitivity. Then, based on a predefined relation between the physical quantity variation sensitivity and the cetane value, the apparatus determines the cetane value of the fuel.
Although the cetane value of the fuel is one of indexes expressing a fuel property, there is a fuel property which cannot be distinguished by the cetane value. Therefore, when the fuel combustion control is performed according to only the cetane value, it is likely that a fuel combustion region is concentrated in a vicinity of an inner surface of a cylinder, so that it is likely that a cooling loss and an emission of soot may not be suppressed.